Experiment 10

Expansion of Gases

Absolute Temperature

Objective:

The objective is to use air expansion to study the linear dependence of volume on temperature for an ideal gas at constant pressure.

Equipment:

A Florence flask, a fitted rubber stopper with two holes, a graduated glass tube with an air-tight sliding cylinder in it, a few digital thermometers, a few 3-liter  containers that stand higher than the flask, a water heater, and a rod-clamp assembly

Theory:

An ideal gas is one that meets the following two conditions:

1) Its temperature is quite above its boiling point, and

2) its pressure is under about 10 atmospheres.  At gas pressure increases, deviation from ideal gas law becomes more significant.

Most gases meet the above conditions.  Hydrogen, oxygen, nitrogen, chlorine, neon, helium, krypton, and more are superheated at Room temperature and have a pressure of 1atmosphere if not under excess compression.  Such gases are called "ideal" or "perfect" because they obey the following simple equation:

PV = nRT

where in SI, P = gas pressure in Pascals, V = gas volume in m3, n = # of moles of gas, R = 8.314 J/(mole K), and T = gas temperature in Kelvin.

When a perfect gas undergoes a process such that its state (P1, V1, and T1) changes to a another state (P2, V2, and T2), we may apply the above equation to each state and then divide the resulting equations side by side as follows:

Note that in Equation (1), both T1 and T2 are absolute temperatures in Kelvin scale (K = ˚C + 273).

Let the volume of a certain amount of an ideal gas be V1 while a temperature t1.   If the gas is heated up to a higher temperature t2 while keeping its pressure constant, its volume becomes V2.   If  t1 and t2 are in Celsius, we may write:

At constant pressure, the graph of V(T) is expected to be a straight line that verifies the linear dependence of volume on temperature.  It is this linearity that allows us to predict the temperature (in Celsius) at which absolute zero should occur.

The device used for this experiment is made of a 500ml Florence flask that is connected to a glass tube in which an air-tight cylinder can slide horizontally.  The purpose is to expand the air inside the flask by heating it up in order to study gas expansion.  Heating up the flask makes its enclosed air to expand.  The air expansion pushes the cylinder inside the glass tube toward the tube's open end.  The tube is graduated and can measure the change in gas volume due to a known change in temperature. 

Note that the thermometer in the flask must be in contact with the air (gas) in it for a long time before you can trust its reading.  This is simply because of lack of strong contact between the probe and the air molecules in the flask.  For this reason, the experiment must be done in a number of steps.  For each step, a separate water container should be used that has already an stabilized water temperature as read by a separate digital thermometer in it.  After the flask is placed in one water container, the gas in the flask picks up the container's temperature fairly quickly ( about a minute or so) while the thermometer in the flask (if one in put in) reaches the containers water temperature after a long time!  Actually, it is not necessary to have a thermometer in the flask.   It is better to have a thermometer in every container that the flask is going to be inserted in.  A diagram of the apparatus is shown below:

 The 3-liter container should be tall enough to keep the water level up to the neck of the flask. This provides a fairly uniform glass temperature for heat transfer to the air inside the flask.

To begin this experiment, each of the 3-liter containers must be halfway filled with water and a thermometer placed in each.  One safe temperature range to work with is say from 20˚C to 40˚C.  If 4 containers are used, for example, let the first one be at the tap water temperature that is less or more around 20˚C. The other containers must be at increasingly higher temperatures, say about 2˚C difference per container.  When the flask is placed in any of the containers, the gas picks up that container's temperature fairly quickly (in a minute or so) during which period the drop in the water temperature is insignificant.

Procedure:

1) Place the rubber stopper on the top of the flask and press down gently for an air-tight fit.

2)  Mark the lower edge of the stopper in order to measure the volume of the air that is to be expanded.  You may skip this step, if the exact volume of air that the flask can hold is already known.  Consult with your lab instructor.

3) Skip this step if Steps 1 and 2 were skipped; otherwise, determine the exact volume of the flask by filling it with water out of a graduated tube up to the rubber stopper marking. 

4) When the flask's air volume is known and the rubber stopper has a tight fit on it, place it (up to its rim) inside the coldest water container.  For this first temperature measurement, wait for five minutes to make sure that the air inside the container attains the same temperature as the water in that container.

5) Now connect the tube-slider assembly to the flask via the rubber connector such that the tube stays in horizontal position at all time.  Use an appropriate support (such as rods and clamps) if needed.  Make sure that the front edge of the slider is at a good starting position and has enough length in front of it to move when gas expands.  Write down the number that has the role of zero.  Also, determine if the front or back of the slider is used to measure volume changes.

6) Add enough hot water to the subsequent containers ( from the 2nd one on...) such that their temperatures have an increasing order of about 2˚C per container as judged by their own thermometers.

7) Record the initial volume and temperature (V1, t1) of the air in the flask taking into account the initial position of the slider. 

8) Knowing the temperature of the 2nd container (about 2˚C higher than the 1st one), remove the flask from the 1st one and place it in the 2nd one.  If the slider does not move, it must be caught in the tube.  If the slider is wet enough, it will move easily.  The slider must also be horizontal.  Wait  about a minute or so until the slider stabilizes its new position.  Record the new data (V2, t2) of the air in the flask. 

9) Continue with the same procedure as in Step 8 for the subsequent containers and record the subsequent V's and t's.

10) For every two subsequent steps, using formula (2), find an accepted value for the new volume and compare it to the measured value of that new volume.  Calculate a %error for it.

11) Plot V(t).

Data:

Given:     αglass =  9.0x10-6 ˚C-1. (This is given here in case the change in the flask's volume needs to be calculated).

Measured:   Vflask

Reading 1 2 3 4 5 6
T (˚C)

 

           
V (cm3)

Measured

           
V (cm3)

Calculated

Not Applicable          
%error on V

 

Not Applicable          

Calculations:

Show your calculations.

Comparison of the Results:

On the basis of the accepted and measured values of x, calculate a percent error.

Conclusion:   To be explained by students.

Discussion:    To be explained by students.